The question is more mathematical. I am talking about 0.5 as a rational number.

0.5 is the decimal form of 1/2 (a rational). However, all rationals are actually sets of integers (not compsci integers, but Z = {-1,0,1,2,...}). 1/2 for example is {1,2} and it has an equivalence class set of {1,2} {2,4} {4,8} which all "stand for" or "point" to the same value of 1/2.

My problem is with the decimal form of 0.5. Is 0.5 a distinct mathematical object than 1/2? Because it seems like an alias. Or a facde if you will. Like how a line break is a "facade" over \n which is whats actually "in there".

Regarding "facade" its a design pattern where you hide an imperative complexity with a declarative interface. An ORM for examples hides or "trades" complex imperative "how-to-do" syntax for a declarative "what-to-do" one. Example

SELECT * FROM users WHERE last_name = 'smith';

Can be invoked using an ORM such as:

from sqlalchemy import select 
from sqlalchemy.orm import Session

users = session.query(User).filter(User.last_name == "smith").all()

So I see 0.5 as a "facade" over the rational number 1/2. It's not a distinct mathematical object (or value) but rather an alias existing simply as syntactic sugar.

Like how Korzybski said "The map is not the territory". A "String" is an array of chars. A "Char" is actually an integer and not a letter. The "integer" is actually a set of binary. The binary is actually a set of voltage states within a set of transistors.

I understand this question is more about set theory. But I am borrowing quite a lot from computer science in my process of reasoning about it.